scholarly journals Modulational Instability of Periodic Standing Waves in the Derivative NLS Equation

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Jinbing Chen ◽  
Dmitry E. Pelinovsky ◽  
Jeremy Upsal
Keyword(s):  
Modulational Instability ◽  
Standing Waves ◽  
Nls Equation ◽  
Periodic Standing Waves

Optical solitons and stability analysis for the generalized fourth-order nonlinear Schrödinger equation

2019 ◽  
Vol 33 (27) ◽  
pp. 1950333
Author(s):  
Xiao-Song Tang ◽  
Biao Li
Keyword(s):  
Nonlinear Dynamics ◽  
Fourth Order ◽  
Continuous Wave ◽  
Modulational Instability ◽  
Optical Solitons ◽  
Singular Solutions ◽  
Nls Equation ◽  
Ansatz Method ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

We consider a generalized fourth-order nonlinear Schrödinger (NLS) equation. Based on the ansatz method, its bright, dark single-soliton is constructed under some constraint conditions. Furthermore, combining the Riccati equation extension approach, we also derive some exact singular solutions. With several parameters to play with, we display the dynamic behaviors of bright, dark single-soliton. Finally, the condition for the modulational instability (MI) of continuous wave solutions for the equation is generated. It is hoped that our results can help enrich the nonlinear dynamics of the NLS equations.

scholarly journals Variational properties and orbital stability of standing waves for NLS equation on a star graph

2014 ◽  
Vol 257 (10) ◽  
pp. 3738-3777 ◽  
Author(s):  
Riccardo Adami ◽  
Claudio Cacciapuoti ◽  
Domenico Finco ◽  
Diego Noja
Keyword(s):  
Standing Waves ◽  
Orbital Stability ◽  
Star Graph ◽  
Nls Equation

scholarly journals A Note on Sign-Changing Solutions to the NLS on the Double-Bridge Graph

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 161
Author(s):  
Diego Noja ◽  
Sergio Rolando ◽  
Simone Secchi
Keyword(s):  
Boundary Conditions ◽  
Standing Waves ◽  
Nls Equation ◽  
Sign Changing Solutions

We study standing waves of the NLS equation posed on the double-bridge graph: two semi-infinite half-lines attached at a circle. At the two vertices, Kirchhoff boundary conditions are imposed. We pursue a recent study concerning solutions nonzero on the half-lines and periodic on the circle, by proving some existing results of sign-changing solutions non-periodic on the circle.

The Low Dimensionality of Time-Periodic Standing Waves in Water of Finite and Infinite Depth

2012 ◽  
Vol 11 (3) ◽  
pp. 1033-1061 ◽  
Author(s):  
Matthew O. Williams ◽  
Eli Shlizerman ◽  
Jon Wilkening ◽  
J. Nathan Kutz
Keyword(s):  
Standing Waves ◽  
Infinite Depth ◽  
Low Dimensionality ◽  
Periodic Standing Waves ◽  
Time Periodic

Modulational instability of ion-acoustic waves in fully relativistic two-component plasma

2015 ◽  
Vol 81 (3) ◽  
Author(s):  
B. Ghosh ◽  
S. Banerjee
Keyword(s):  
Growth Rate ◽  
Acoustic Waves ◽  
Relativistic Effect ◽  
Modulational Instability ◽  
Perturbation Technique ◽  
Multiple Scale ◽  
Nls Equation ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Component Plasma

Nonlinear amplitude modulation of ion-acoustic waves (IAWs) in a fully relativistic unmagnetized two-fluid plasma has been theoretically studied by using complete set of fully relativistic dynamic equations. To describe the nonlinear evolution of the wave envelope a nonlinear Schrödinger (NLS) equation is derived by using standard multiple scale perturbation technique. Using this equation it is shown that the wave becomes modulationally unstable as the wavenumber exceeds certain critical value. This critical wavenumber is found to decrease with increase in relativistic effect. The instability growth rate has also been calculated numerically for different values of plasma drift velocity. The growth rate is shown to decrease with increase in the relativistic effect.

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